Computational Complexity Theory

  1. Time Complexity Classes
    1. Polynomial Time Class P
      1. Formal Definition
        1. Tractability Interpretation
          1. Closure Properties
            1. Robustness Across Models
              1. Examples of P Problems
                1. Sorting Algorithms
                  1. Graph Algorithms
                    1. Linear Programming
                      1. Primality Testing
                        1. Maximum Flow
                      2. Nondeterministic Polynomial Time Class NP
                        1. Verifier-Based Definition
                          1. Certificate Verification
                            1. Polynomial-Time Verifiers
                            2. Nondeterministic Machine Definition
                              1. Acceptance Conditions
                                1. Computation Paths
                                2. Relationship Between Definitions
                                  1. Closure Properties
                                    1. Examples of NP Problems
                                      1. Boolean Satisfiability
                                        1. Graph Problems
                                          1. Number Theory Problems
                                            1. Optimization Problems
                                          2. Complement Class co-NP
                                            1. Definition and Characterization
                                              1. Relationship to NP
                                                1. Closure Properties
                                                  1. Examples
                                                    1. Tautology Problem
                                                      1. Graph Non-colorability
                                                    2. P versus NP Problem
                                                      1. Formal Problem Statement
                                                        1. Consequences of P = NP
                                                          1. Consequences of P ≠ NP
                                                            1. Millennium Prize Problem
                                                              1. Current Research Approaches
                                                                1. Barriers to Resolution

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                                                              4. Complexity Measurement

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                                                              6. Reducibility and NP-Completeness